Humans have always known that which goes up must
come down. Sir Isaac Newton converted this knowledge into mathematical law.
However, this fact has largely disappointed our species, and thus we devise new
ways to counteract gravitational force. From the creation of the catapult to the
invention of the airplane, man has constantly fought against nature. The latest
step in our struggle is the Pneumatic Cannon. We, being the inquisitive people
we are, search for ways to improve the efficiency of the aforementioned cannon.
Thus, the question arises: “What barrel length will maximize the range of a
juggling ball fired from the cannon?”

While mulling around on the internet, we ran across
some information on air cannons, and also found that another group of people,
labeled #3 in our bibliography, has previously done research in our subject of
study. While researching their experiment, we found that they did not find any
correlation between barrel length and range. We decided that they did not make
their barrel lengths extreme enough to form any correlation, so we improved on
their experiment by making our barrels either longer or shorter than theirs.
We can use linear kinematics to find the distance the projectile travels.

Using the equation s = ut + ½ at2 we can find the vertical range of
the projectile. Finally, we reach the dependent variable of our experiment. We
plan to compare the distances that the projectile reaches and the length of the
barrel of the cannon. Hence, we arrive at our hypothesis-

We took different lengths of pipe and turned them into barrels for our cannon.
More specifically, we cut lengths of pipe that were 1’, 2’, 3’, and 7’ in
length. The reason for this was funding, and we wanted to get the two extremes
in length, extremely short and extremely long. We designed the cannon as a
modular piece of equipment, which made repairs extremely easy, except that more
pieces could break because of it. We also shot two different objects, both
juggling balls, out of our cannon in an effort to avoid damage to the projectile
and also to make sure there was nothing special about the particular object we
shot that would make it go higher or otherwise skew our data. We labeled them
balls #1 and #2. When we collected enough data, we took the average hang times
of the two objects, and found the average final velocities of the balls in
different barrels.Oh yeah, we always
shot our balls at 80 psi.

Because time is
directly proportional to range, we found that by graphing the times of the
balls, we could see which ball was in the air the longest, which must have gone
the highest. By analyzing the graph of the times, we found that the ideal
barrel length will be within half a foot of two feet, that is between 1.5’ and
2.5’. We predict that there will be a plateau effect, and after 2.5’, the range
of the projectile will drop suddenly. While it would be nice to test this
theory, the availability of funding was rather limited, which made it such that
we could not afford the amount of materials that such an undertaking would
incur. We realized that because we recorded the times that the objects were in
the air, we could simply use linear kinematics to discern the ranges that they
reached. By using the equation v=u+at, where v=0, we could figure out the
initial velocity. Because half the time in the air is spent coming down, we
simply found the initial velocity by setting the final velocity at zero, using
the accepted acceleration due to gravity, 9.8m/s2, as a, then using
half the time we recorded. Then, using the final velocities we found, we
calculated the range using the equation v2=u2+2as, where
u, v and a are the same as in the other equation, and s is the vertical
displacement. We noticed that there is a peak in the data at a 2 foot barrel
length, and by making a graph of best fit , and then looking at that graph, we
decided that the graph will peak around approximately .5 feet within either side
of the 2 foot barrel length.

Our hypothesis, that barrel length affects the range of the projectile, was
correct, insofar as we were able to test it. We came up with many theories to
explain the phenomenon. Our first theory is that the friction between the ball
and the sides of the barrel causes the ball to slow down, and thus, not go as
high. This cannot be the entire explanation however, because it does not
explain the peak in the data at the 2-foot barrel length. Another theory lies
in Pascal’s research. Because the pressure in the compression chamber is
constant, then the amount of pressure at the end of the barrel is variable
depending on the length of it. When the barrel is longer, there is more volume,
and because PV=PV, the amount of pressure behind the ball at the end of the
barrel is lessened. However, we still have the problem of the smaller ranges
with smaller tubes. Our hypothesis for that is that the pressure is higher
behind the ball, yes, but because there is less time for acceleration, the ball
does not go as high. An analogy for this would be punching the accelerator in
your car for one second rather than holding it at 75% acceleration for 3
seconds. Yes, the acceleration is higher at maximum acceleration, but the
increased time at a smaller acceleration still results in a higher velocity.
Also, the more time there is a force being applied behind an object, gravity
gets less of a chance to take over. There are problems inherent in our
experiment, just as there are in any. Specifically, we ran into problems
timing, and also with getting the correct pressure in the compression chamber.
We solved these problems by using a pressure gauge, and also by having multiple
timers. Our other major problem was a lack of funding, coupled with time
constraints. We were unable to solve these problems, but we did the best we
could given the situation presented to us. In the future, if we were ever to
redo this experiment, we decided that having a computer time the flight of the
ball, and having a computer fill the compression chamber with a perfectly
constant pressure, we would be able to gather more accurate data. Also, we
decided that we would use more barrels, take more data, and then try changing
the pressure in the chamber to see what affects the range of the projectiles
launched from our cannon. After all, launching spark plugs a quarter mile
is all in the interests of science, right?

www.mla.org
<This website is important in explaining how to write bibliographies>

Giancoli, Douglas. “Pressure in Fluids”. Physics:
Principles with Applications. Ed. Corey, Paul F. 1998. New Jersey:
Prentice Hall Press. <This book was our class text, and we used it to find
things about pressure and fluids and stuff>

http://www.bosik.com/impact.htm
<Take a look at what happens when you make an EXTREME pneumatic cannon!
Also the practical side to having a air powered howitzer...>